If two rods of length L and 2L having coefficients of linear expansion $\mathrm{\alpha }$ and $2\mathrm{\alpha }$ respectively are connected so that their total length becomes 3L, the average coefficient of linear expansion of the composition of rods equals:

1.  $\frac{3}{2}\mathrm{\alpha }$

2.  $\frac{5}{2}\mathrm{\alpha }$

3.  $\frac{5}{3}\mathrm{\alpha }$

4.  none of these

A body cools from a temperature of \(3T\) to \(2T\) in \(10\) minutes. The room temperature is \(T\). Assuming that Newton's law of cooling is applicable, the temperature of the body at the end of the next \(10\) minutes will be:

If the radius of a star is \(R\) and it acts as a black body, what would be the temperature of the star at which the rate of energy production is \(Q\)?
1. \(\frac{Q}{4\pi R^2\sigma}\)
2. \(\left(\frac{Q}{4\pi R^2\sigma}\right )^{\frac{-1}{2}}\)
3. \(\left(\frac{4\pi R^2 Q}{\sigma}\right )^{\frac{1}{4}}\)
4. \(\left(\frac{Q}{4\pi R^2 \sigma}\right)^{\frac{1}{4}}\)

Liquid oxygen at \(50\) K is heated up to \(300\) K at a constant pressure of \(1\) atm. The rate of heating is constant. Which one of the following graphs represents the variation of temperature with time?

1.		2.
3.		4.

The temperature of a body on the Kelvin scale is found to be x K. When it is measured by a Fahrenheit thermometer, it is found to be x$°$F, then the value of x is:
1. 40
2. 313
3. 574.25
4. 301.25

On a new scale of temperature, which is linear and called the \(\mathrm{W}\) scale, the freezing and boiling points of water are \(39^\circ ~\mathrm{W}\)$$and \(239^\circ ~\mathrm{W}\) respectively. What will be the temperature on the new scale corresponding to a temperature of \(39^\circ ~\mathrm{C}\) on the Celsius scale?
1. \(78^\circ ~\mathrm{C}\)
2. \(117^\circ ~\mathrm{W}\)
3. \(200^\circ ~\mathrm{W}\)
4. \(139^\circ ~\mathrm{W}\)

Which of the following graphs correctly represents the relation between \(ln~E\) and \(ln~T\) where \(E\) is the amount of radiation emitted per unit time from a unit area of a body and \(T\) is the absolute temperature?\(\left (Take~\sigma =5.67\times 10^{-8} ~W~m^{-2}~K^{-4}~and~0<\epsilon <1 \right )\)

1.		2.
3.		4.	Both 1 and 3

The energy distribution E with the wavelength $\left(\mathrm{\lambda }\right)$ for the black body radiation at temperature T Kelvin is shown in the figure. As the temperature is increased the maxima will:
     

A block of metal is heated to a temperature much higher than the room temperature and allowed to cool in a room free from air currents. Which of the following curves correctly represents the rate of cooling?

1.		2.
3.		4.

One end of a copper rod of uniform cross-section and of length 3.1 m is kept in contact with ice, and the other end with water at \(100^{\circ}\mathrm{C}\). At what point along its length should a temperature of \(200^{\circ}\mathrm{C}\) be maintained so that in steady-state, the mass of ice melting be equal to that of the steam produced in the same interval time? (Assume that the whole system is insulated from the surroundings. Latent heat of fusion of ice and vaporisation of water are 80 cal/gm and 540 cal/gm respectively)